In many networked systems such as wireless sensors, robots, smart grids, water distribution, and vehicular networks, decision variables must often be optimized by algorithms that need to be fast, simple, and robust to errors and noises, both in a centralized and in a distributed set-up. In this lecture, a new simple optimization theory, named Fast-Lipschitz optimization, is introduced for a novel class of both convex and non-convex scalar and multi-objective optimization problems that are pervasive in these networked systems. Fast-Lipschitz optimization can be applied to both centralized and distributed optimization. Fast-Lipzhitz optimization solvers exhibit a low computational and communication complexity when compared to existing solution methods, which makes this new optimization method very useful in wireless sensor networks. In particular, compared to traditional Lagrangian methods, which often converge linearly, the convergence time of centralized Fast-Lipschitz algorithms is superlinear. Distributed Fast-Lipschitz algorithms converge fast, as opposed to traditional Lagrangian decomposition and parallelization methods, which generally converge slowly and at the price of many message passings among the nodes. In both cases, the computational complexity is much lower than traditional Lagrangian methods.